Re: Beginner Question

*To*: mathgroup at smc.vnet.net*Subject*: [mg66587] Re: Beginner Question*From*: "Scout" <Scout at nodomain.com>*Date*: Sun, 21 May 2006 00:29:29 -0400 (EDT)*References*: <e4mmb8$6iu$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

"akil" <akil39 at gmail.com> news:e4mmb8$6iu$1 at smc.vnet.net... > Hi, > > Suppose I have three 2D points A, B, C. > And two points, namely A and B form a line. > > How can I determine in mathematica on which side, (so which half-plane > formed by) of the line, point C is. > > So when I input three points I want to know if the third point is on the > left or right side of the half plane formed by the line (ray) A,B. > > Appreciate any help. > Well, the Dot Product can do better the work. Below it's a simple procedure: Let's start with a test function on a 2D point: In[1]:= point2DQ[x_] := VectorQ[x] && (Length[x] == 2); Now, we can write the function that will decide on the A,B,C points: In[2]:= whichPart[a_?point2DQ, b_?point2DQ, c_?point2DQ] := Module[{v1 = c - a, v2 = b - a}, (v1 . v2) / (Norm[v1]*Norm[v2]) ]; If the whichPart[] function gives a negative number (< 0), then the C point is on the right if you move from A to B; if it gives a positive number (> 0), then the C point is on the left if you move always from A to B; and if it equals 1, then the 3 points are on the same line. Best, ~Scout~